If nothing else, go to a bar called Next Apache. It's on the same street as a pretty good hostel/restuarant. It has lots of books to read/buy, the Economist and cheap, nice beer, cool bar staff, yeah.
The clock museum is good and you get free postcards.
The castle is currently closed I think.
There's a cool upsidedown pyramid building and a UFO tower on a bridge. Lots of the Jewish nice parts were demolished to make the bridge:(
the cathedral has some really cool choir carvings with chimps playing bagpipes, and some snazzy monstrances, embroidery and decorative stuff.
There's an art nouveau bright blue church.

Go to the spa town Piescany for some outdoor swimming and Modra for wine. Piescany is very badly signposted. Vienna is only 40 minutes on the train too.